scholarly journals STRESS SENSITIVITY ANALYSIS OF FRACTAL POROUS MEDIA BASED ON THE ELASTO-PLASTIC THICK-WALLED CYLINDER MODEL

Fractals ◽  
2021 ◽  
Vol 29 (03) ◽  
pp. 2150162
Author(s):  
ZHAOQIN HUANG ◽  
XIN SU ◽  
YANCHAO LI ◽  
KAI ZHANG ◽  
JUN YAO
Keyword(s):  
Porous Media ◽  
Fractal Theory ◽  
Fractal Model ◽  
Stress Sensitivity ◽  
Proposed Model ◽  
Cylinder Model ◽  
Stress Cycles ◽  
Dependent Flow ◽  
Stress Dependent ◽  
Walled Cylinder

The stress-dependent flow and transport behaviors of porous media are ubiquitous in various scientific and engineering applications. It has been shown that the change of effective stress has important effects on the permeability and porosity of porous media. In this paper, a new stress sensitivity model for porous media is developed based on the fractal theory and the elasto-plastic thick-walled cylinder model. The proposed model is able to predict the elasto-plastic deformation of the fractal porous media under loading–unloading stress cycles, which plays a crucial role on the permanent variations of the permeability and porosity. It is found that the permeability of stress-sensitivity porous media is related to the capillary fractal dimension, capillary fractal tortuosity dimension, minimum and maximum capillary diameters, Young’s modulus and Poisson’s ratio of capillary. Each parameter has a clear physical meaning. The validity of the developed fractal model is verified by comparing the model predictions with the available experimental data.

A stress sensitivity model for the permeability of porous media based on bi-dispersed fractal theory

2018 ◽  
Vol 29 (02) ◽  
pp. 1850019 ◽  
Author(s):  
X.-H. Tan ◽  
C.-Y. Liu ◽  
X.-P. Li ◽  
H.-Q. Wang ◽  
H. Deng
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Stress Sensitivity ◽  
Maximum Diameter ◽  
Proposed Model ◽  
Fractal Parameters ◽  
Stress Changes ◽  
Capillary Bundle ◽  
Definition Of

A stress sensitivity model for the permeability of porous media based on bidispersed fractal theory is established, considering the change of the flow path, the fractal geometry approach and the mechanics of porous media. It is noted that the two fractal parameters of the porous media construction perform differently when the stress changes. The tortuosity fractal dimension of solid cluster [Formula: see text] become bigger with an increase of stress. However, the pore fractal dimension of solid cluster [Formula: see text] and capillary bundle [Formula: see text] remains the same with an increase of stress. The definition of normalized permeability is introduced for the analyzation of the impacts of stress sensitivity on permeability. The normalized permeability is related to solid cluster tortuosity dimension, pore fractal dimension, solid cluster maximum diameter, Young’s modulus and Poisson’s ratio. Every parameter has clear physical meaning without the use of empirical constants. Predictions of permeability of the model is accordant with the obtained experimental data. Thus, the proposed model can precisely depict the flow of fluid in porous media under stress.

Fractal analysis of permeability near the wall in porous media

2014 ◽  
Vol 25 (07) ◽  
pp. 1450021 ◽  
Author(s):  
Mingchao Liang ◽  
Boming Yu ◽  
Li Li ◽  
Shanshan Yang ◽  
Mingqing Zou
Keyword(s):  
Porous Media ◽  
Pore Size ◽  
Pore Space ◽  
Fractal Theory ◽  
Particle Diameter ◽  
Fractal Dimensions ◽  
Fractal Model ◽  
Proposed Model ◽  
Medium Porosity ◽  
The Relationship

In this paper, a fractal model for permeability of porous media is proposed based on Tamayol and Bahrami's method and the fractal theory for porous media. The proposed model is expressed as a function of the mean particle diameter, the length along the macroscopic pressure drop in the medium, porosity, fractal dimensions for pore space and tortuous capillaries, and the ratio of the minimum pore size to the maximum pore size. The relationship between the permeability near the wall and the dimensionless distance from the wall under different conditions is discussed in detail. The predictions by the present fractal model are in good agreement with available experimental data. The present results indicate that the present model may have the potential in comprehensively understanding the mechanisms of flow near the wall in porous media.

A Semi-Analytical Fractal-Fractional Mathematical Model for Multi-Fractured Horizontal Wells in Coalbed Methane Reservoirs

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Ruizhong Jiang ◽  
Xiuwei Liu ◽  
Xing Wang ◽  
Qiong Wang ◽  
Yongzheng Cui ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Coalbed Methane ◽  
Fractal Theory ◽  
Superposition Principle ◽  
Horizontal Wells ◽  
Clean Energy ◽  
Stress Sensitivity ◽  
Element Discretization ◽  
Proposed Model ◽  
Fractured Horizontal Wells

Abstract Coalbed methane (CBM) which is clean energy has received great emphasis recently, and the multi-fracturing technology is widely applied in the exploitation of CBM. Due to the complexity, the randomness, and the anisotropism of the porous medium and the anomalous diffusion process, the fractal theory and fractional calculus are utilized to establish a semi-analytical fractal-fractional mathematical model considering the stress sensitivity of the cleat system for multi-fractured horizontal wells in CBM reservoirs. Through line-sink theory, Pedrosa transformation, perturbation theory, Laplace transformation, element discretization, superposition principle, and Stehfest numerical inversion, the pressure-transient analysis curves are plotted in the double logarithmic coordinates. By comparing with the existing model, the validation of the proposed model is illustrated. Also, nine flowing stages are identified according to different characteristics. Then, sensitivity analysis is conducted and influence laws are summarized. At last, a field application is introduced to furtherly verify the reliability of the proposed model. The relevant results analysis can provide some new significant guidance for interpreting the field data more precisely.

A DIFFUSIVITY MODEL FOR GAS DIFFUSION IN DRY POROUS MEDIA COMPOSED OF CONVERGING–DIVERGING CAPILLARIES

Fractals ◽  
2016 ◽  
Vol 24 (03) ◽  
pp. 1650034 ◽  
Author(s):  
SHIFANG WANG ◽  
TAO WU ◽  
YONGJU DENG ◽  
QIUSHA ZHENG ◽  
QIAN ZHENG
Keyword(s):  
Experimental Data ◽  
Porous Media ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Knudsen Diffusion ◽  
Fractal Model ◽  
Gas Diffusion ◽  
Pore Area ◽  
Relative Diffusivity ◽  
Fluctuation Amplitude

Gas diffusion in dry porous media has been a hot topic in several areas of technology for many years. In this paper, a diffusivity model for gas diffusion in dry porous media is developed based on fractal theory and Fick’s law, which incorporates the effects of converging–diverging pores and tortuous characteristics of capillaries as well as Knudsen diffusion. The effective gas diffusivity model is expressed as a function of the fluctuation amplitude of the capillary cross-section size variations, the porosity, the pore area fractal dimension and the tortuosity fractal dimension. The results show that the relative diffusivity decreases with the increase of the fluctuation amplitude and increases with the increase of pore area fractal dimension. To verify the validity of the present model, the relative diffusivity from the proposed fractal model is compared with the existing experimental data as well as two available models of Bruggeman and Shou. Our proposed diffusivity model with pore converging–diverging effect included is in good agreement with reported experimental data.

FRACTAL ANALYSIS OF THE PENETRATION FLOW THROUGH MICRO-NANO POROUS GASKETS WITH EFFECTS OF SLIPPAGE AND STRESS-SENSITIVITY

Fractals ◽  
2019 ◽  
Vol 27 (03) ◽  
pp. 1950031
Author(s):  
XIAOMING HUANG ◽  
JIAWEI SUN ◽  
CHUNYU SHI ◽  
YANG DU ◽  
GUOLIANG XU
Keyword(s):  
Porous Media ◽  
Pore Size ◽  
Transport Theory ◽  
Stress Sensitivity ◽  
Sealing Material ◽  
Proposed Model ◽  
Slippage Effect ◽  
Flow Through ◽  
Gas Penetration ◽  
Flexible Graphite

The airtightness of non-metallic sealing structures undergoing harsh conditions is very crucial to the reliability of equipment in many industrial fields. In this study, the gas penetration through a non-metallic sealing material (NSM) with micro-nano porous structure under stress was investigated in detail based on the transport theory of fractal porous media. A complete theoretical model for predicting the stress sensitivity of the gasket permeability was developed, in which the slippage effect was of concern due to very fine pore size. The permeability of a flexible graphite gasket under different stresses was numerically predicted via scanning electron microscopy (SEM) and image processing. The influencing factors on the permeability of the NSM were analyzed quantitatively and good agreements with existing experimental results demonstrate the validity of the proposed model. Since the effects of the pore-size distribution and flow pattern regime were taken into account, the parameters of the model had a clear physical meaning and the model was suitable for determining the mechanism of penetration leakage through the NSM. In addition, the model could also be used for the analysis of other tight porous media with complex microstructure under stress deformation.

A FRACTAL MODEL FOR KOZENY–CARMAN CONSTANT AND DIMENSIONLESS PERMEABILITY OF FIBROUS POROUS MEDIA WITH ROUGHENED SURFACES

Fractals ◽  
2019 ◽  
Vol 27 (07) ◽  
pp. 1950116 ◽  
Author(s):  
BOQI XIAO ◽  
YIDAN ZHANG ◽  
YAN WANG ◽  
GUOPING JIANG ◽  
MINGCHAO LIANG ◽  
...  
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Fluid Transport ◽  
Fractal Theory ◽  
Fractal Model ◽  
Physical Mechanisms ◽  
Relative Roughness ◽  
Fibrous Porous Media ◽  
Effect Of Surface ◽  
Good Agreement

In this paper, fluid transport through fibrous porous media is studied by the fractal theory with a focus on the effect of surface roughness of capillaries. A fractal model for Kozeny–Carman (KC) constant and dimensionless permeability of fibrous porous media with roughened surfaces is derived. The determined KC constant and dimensionless permeability of fibrous porous media with roughened surfaces are in good agreement with available experimental data and existing models reported in the literature. It is found that the KC constant of fibrous porous media with roughened surfaces increases with the increase of relative roughness, porosity, area fractal dimension of pore and tortuosity fractal dimension, respectively. Besides, it is seen that the dimensionless permeability of fibrous porous media with roughened surfaces decreases with increasing relative roughness and tortuosity fractal dimension. However, it is observed that the dimensionless permeability of fibrous porous media with roughened surfaces increases with porosity. With the proposed fractal model, the physical mechanisms of fluids transport through fibrous porous media are better elucidated.

SOME FRACTAL CHARACTERS OF POROUS MEDIA

Fractals ◽  
2001 ◽  
Vol 09 (03) ◽  
pp. 365-372 ◽  
Author(s):  
BOMING YU ◽  
JIANHUA LI
Keyword(s):  
Porous Media ◽  
Fractal Theory ◽  
Unified Model ◽  
Counting Method ◽  
Statistical Property ◽  
Box Counting ◽  
Fractal Media ◽  
Proposed Model ◽  
Theoretical Predictions ◽  
Box Counting Method

In this paper, a unified model for describing the fractal characters of porous media is deduced. The theoretical predictions from the proposed unified model are compared with those from the previous models and from the box-counting method. The results from the proposed model are found to be in good agreement with both the previous models and box-counting method. The results also indicate that the proposed unified model is applicable to both the exactly and statistically self-similar fractal media. A statistical property of porous media is also described based on the basic fractal theory and technique. A criterion, for determining whether a porous medium can be characterized by fractal theory and technique or not, is proposed based on the fractal statistical property.

PERMEABILITY PREDICTION IN ROUGHENED FRACTURES UNDER STRESS CONDITION USING FRACTAL MODEL

Fractals ◽  
2019 ◽  
Vol 27 (03) ◽  
pp. 1950030 ◽  
Author(s):  
GANG LEI ◽  
NAI CAO ◽  
QINGZHI WEN
Keyword(s):  
Stress Condition ◽  
Fractal Model ◽  
Coupled Flow ◽  
Permeability Model ◽  
Microstructural Parameters ◽  
Rough Fracture ◽  
Proposed Model ◽  
Stress Dependent ◽  
Rock Lithology ◽  
Good Agreement

The prediction of permeability in rough fracture under stress condition presents ever more of a challenge in various scientific and engineering fields. However, up to now, the essential controls on stress-dependent permeability of rough fracture are not determined. In order to find a relationship between the microstructure and the permeability of rough fracture, an analytical method for the permeability of roughened fracture under stress condition is proposed based on the fractal model. The validity of the proposed model is obtained by the good agreement between the simulated results and the experimental data. Compared with the previous models, our model takes into account more factors, including the influence of the microstructural parameters of rough fracture and rock lithology. This paper presents that (1) the rock with soft lithology can yield smaller normalized permeability, (2) normalized permeability decreases with the increases of percent of smaller rough elements. The fractal permeability model can reveal more mechanisms that affect the coupled flow deformation behavior in the fractured porous media.

A novel fractal model for the prediction and analysis of the equivalent thermal conductivity in wood

Holzforschung ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jingyao Zhao ◽  
Liangyan Guo ◽  
Yingchun Cai
Keyword(s):  
Thermal Conductivity ◽  
Pore Structure ◽  
Structural Parameters ◽  
Geometric Model ◽  
Fractal Theory ◽  
Wood Properties ◽  
Fractal Model ◽  
Equivalent Thermal Conductivity ◽  
Proposed Model ◽  
Aperture Distribution

Abstract This study proposes a new fractal model to improve the accuracy of equivalent thermal conductivity (ETC) prediction for wood and determine how the wood’s pore structure influences ETC. Using fractal theory and mercury injection porosimetry data, a fractal model for the geometry of the wood’s pore structure was built. The geometric model was then transformed into an equivalent thermal resistance model to calculate ETC. The calculations produced an explicit expression for ETC derived from the wood’s structural parameters including the minimum and maximum pore apertures, aperture distribution, porosity, and fractal dimension. The model also includes a probability factor. The simulated ETC produced by the model was validated by experiments and it was found to be in good agreement with these. These simulation results will be used to study the influence of several factors on ETC. The proposed model has the potential to be able to predict and analyzing other wood properties such as its electrical conductivity, diffusivity, and permeability and the model can likely also be used to analyze other porous materials.

scholarly journals Examination of the fractal model for streaming potential coefficient in porous media

2019 ◽  
Vol 35 (1) ◽  
Author(s):  
Luong Duy Thanh
Keyword(s):  
Experimental Data ◽  
Porous Media ◽  
Zeta Potential ◽  
Streaming Potential ◽  
Fractal Model ◽  
Potential Coefficient ◽  
Proposed Model ◽  
Alternative Approach ◽  
High Fluid ◽  
Good Agreement

In this work, the fractal model for the streaming potential coefficient in porous media recently published has been examined by calculating the zeta potential from the measured streaming potential coefficient. Obtained values of the zeta potential are then compared with experimental data. Additionally, the variation of the streaming potential coefficient with fluid electrical conductivity is predicted from the model. The results show that the model predictions are in good agreement with the experimental data available in literature. The comparison between the proposed model and the Helmholtz-Smoluchowski (HS) equation is also carried out. It is seen that that the prediction from the proposed model is quite close to what is expected from the HS equation, in particularly at the high fluid conductivity or large grain diameters. Therefore, the model can be an alternative approach to obtain the zeta potential from the streaming potential measurements.

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